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Science & Mathematics

The Museum's collections hold thousands of objects related to chemistry, biology, physics, astronomy, and other sciences. Instruments range from early American telescopes to lasers. Rare glassware and other artifacts from the laboratory of Joseph Priestley, the discoverer of oxygen, are among the scientific treasures here. A Gilbert chemistry set of about 1937 and other objects testify to the pleasures of amateur science. Artifacts also help illuminate the social and political history of biology and the roles of women and minorities in science.

The mathematics collection holds artifacts from slide rules and flash cards to code-breaking equipment. More than 1,000 models demonstrate some of the problems and principles of mathematics, and 80 abstract paintings by illustrator and cartoonist Crockett Johnson show his visual interpretations of mathematical theorems.

Lewis M. Rutherfurd (1816-1892) was an independent astronomer in New York City who began making diffraction gratings around 1871 and distributing them freely to astronomers and physicists in the United States and abroad. By 1875 he was producing gratings with 17,280 lines per inch. This example is a steel plate measuring 1.75 inches square overall, with the ruled area occupying the central 1 inch square. The plate is marked "Dec. 22, 1877" and a card in the box is marked "17,280 No. 1".

Charles A. Young, the professor of astronomy at the College of New Jersey (later Princeton University), acquired this diffraction grating in 1878. The speculum metal plate measures 3 inches square overall, with the grating measuring 1.75 inch square. It is marked: "May 28, 1878" and "16,560 spaces" and "8648 per inch" and "Manf. by D. C. Chapman with Mr. Rutherfurd's Engine." Daniel C. Chapman was the mechanic who operated the ruling engine designed by Lewis M. Rutherfurd.

This is one of the earliest gratings made by Lewis M. Rutherfurd, and one of three that the pioneer astrophysicist, Henry Draper, acquired in the fall of 1872. The glass plate measures 1.5 inches square overall, with the grating measuring 1⅛ inches square, and is marked "12960 to the inch Oct. 16, 1872 L. M. Rutherfurd."

This is one of the earliest gratings made by Lewis M. Rutherfurd, and one of three that the pioneer astrophysicist, Henry Draper, acquired in the fall of 1872. The glass plate measures 2 inches square; the grating surface is 31/32 inches wide; the grooves are 13/16 inches long. The plate is marked "6480 per inch 90 L. M. Rutherfurd."

Benjamin Peirce, Harvard professor of mathematics and third superintendent of the U.S. Coast Survey, was on good terms with Louis Agassiz, the charismatic Swiss naturalist who taught at Harvard’s Lawrence Scientific School and served as the founding director of Harvard’s Museum of Comparative Zoology. Writing to Agassiz in February 1871, Peirce announced that the Coast Survey was about “to send a new iron steamer round to California” and asked if Agassiz would “go in her, and do deep-sea dredging all the way around?” Since Agassiz had conducted several research projects under the aegis of the Coast Survey, Peirce expected that he would accept this new proposition. The new ship, the first iron-hulled vessel owned by the Survey, was designed to dredge at depths never before reached. Named the Hassler after the first superintendent of the Coast Survey, the ship's maiden voyage would be known as the Hassler Expedition.

The Coast Survey had the largest budget of any 19th-century American scientific organization, and employed more scientists, both directly and indirectly. But aware of Congressional concerns about how federal funds should be spent, the Survey tended to hide its science behind its more practical activities. Thus while the Hassler sailed from the East Coast where it was built to the Pacific Coast where it would see service, the ship` could transport Agassiz, his wife, and several colleagues and assistants. But Agassiz had to raise the $20,000 needed to preserve the many specimens they hoped to collect and send back to the States for further study. Most of these specimens went to the Museum of Comparative Zoology and the Smithsonian Institution.

The Hassler left the Boston Navy Yard on Dec. 4, 1871 and made land in San Francisco some nine months later. Despite equipment failure and various delays, much was accomplished on the Expedition. The Coast Survey aimed to discover the origin of the Gulf Stream, determine the greatest depth of the Atlantic, exploring the coasts of Patagonia, chart the dangerous currents in and around the Straits of Magellan, and trace Darwin’s steps in the Galapagos Islands. Agassiz was especially interested in evidence of glacial action in the Southern Hemisphere (which he found), and evidence that might disprove Darwin’s theory of evolution (which he did not).

The Hassler left the Boston Navy Yard on Dec. 4, 1871 and made land in San Francisco some nine months later. Despite equipment failure and various delays, much was accomplished on the expedition. The Coast Survey aimed to discover the origin of the Gulf Stream, determine the greatest depth of the Atlantic, explore the coasts of Patagonia, chart the dangerous currents in and around the Straits of Magellan, and trace Darwin’s steps in the Galapagos Islands. Agassiz was especially interested in evidence of glacial action in the Southern Hemisphere (which he found), and evidence that might disprove Darwin’s theory of evolution (which he did not).

This large, carefully posed and somewhat manipulated photograph was made while plans for the expedition were underway. Agassiz is seated at the left of a round table, Peirce stands behind the table, and Carlile Patterson, the Hydrographic Inspector of the Coast Survey (and the man who had planned the internal arrangements of the new ship) sits at right. These men seem to be discussing a chart attached to which an obviously enlarged piece of paper carries the hand-written inscription “Instructions for Expd.” and “To. Prof. L. Agassiz / from Captain C. Patterson / Yours respectfully / Benjamin Peirce / Superintendent.”

The text at bottom of the photograph reads “Entered according to Act of Congress in the year 1871 by A. SONREL, in the Office of the Librarian of Congress at Washington, D.C.” This refers to the federal copyright act of 1870. That image is now in the Prints and Photographs Division of the Library of Congress. It is identical to our copy, but has an “A. Sonrel” signature in the lower left.

Antoine Sonrel (d. 1879) was an accomplished scientific illustrator who had worked with Agassiz in Neuchâtel, followed him to the United States, and prepared the lithographic plates for several of his publications. He was also an accomplished photographer who did commercial and scientific work. Several Agassiz cartes-de-visite photographs were taken by in Sonrel’s Boston studio. Another Sonrel photograph dated 1871, probably taken on the same day as our image, shows Agassiz and Peirce, the former seated in a chair, and the latter standing with his right hand on a globe pointing to Boston. And, as our image indicates, Sonrel, like many photographers then as now, enjoyed manipulating images. Another Sonrel photograph shows Agassiz talking to Agassiz across a table. Yet another shows an unidentified man playing chess with himself.

According to a note on the back of the frame, this photograph was purchased at an auction of the effects Mrs. John Cummings in 1928. The reference is to Mary Phelps Cowles (1839-1927), a woman of culture and wealth who was married to Adino Brackett Hall, a Boston physician, and then John Cummings, a landowner in Woburn, Ma.

The title of this bound set of tables well describes the goal of the author. Printed in gold color on the front of the reddish brown binding, it reads: AUTOMATIC ARITHMETIC: (/) A NEW SYSTEM (/) FOR (/) MULTIPLICATION AND DIVISION (/) WITHOUT MENTAL LABOUR (/) AND (/) WITHOUT THE USE OF LOGARITHMS. In 1879, when the book was published, London accountants like the author John Sawyer multiplied and divided large numbers by consulting tables of logarithms. They or their clerks also carried out calculations by hand. However, the results obtained from logarithm tables were only approximate, and hand calculations might be erroneous. Calculating machines had sold commercially in England from the 1850s, but they were expensive and required maintenance.

As an alternative, Sawyer proposed and patented his system of “automatic arithmetic.” This was an unusually designed arrangement of multiplication tables that allowed one to read off the partial products needed to solve multiplication problems.

Sawyer’s system consisted of eighteen pages of instructions bound with ten sheets of heavier paper. Each of these heavier pieces is cut horizontally to form nine rows. The topmost and shortest strip of paper has the digits from 1 to 9 in one row and then a row of nine 00s. The eight other strips on this page simply have a row of nine 00s. The figures in each succeeding row are shifted one place to the right from those immediately above them.

On the second page of the tables, the slips are slightly longer and are marked 1 on the right end. The topmost slip has the digits from 1 to 9 in a row, as well as a row of multiples of 1 running from 01 to 09. The slips below it have the multiples of 1, shifted one place to the right in each successive row. Similarly, the third page has still longer slips, marked 2 on the right end. The topmost slip has the digits from 1 to 9 in a row, and then multiples of two. The slips below this have multiples of two, shifted one place to the right from the row above. The remaining slips follow a similar pattern.

To multiply using the tables, one turns the top pile of slips to the slips for the leftmost digit of the multiplicand, the slips in the second pile to the second digit of the number and so forth. To multiply by a single digit, one adds the partial products found on the slips turned. Further instructions suggest how the slips can be used to multiply by larger number of digits and to divide.

Sawyer obtained patents for his invention in the United Kingdom in 1877 and in the United States in 1879. It was advertised in the British journal The Accountant, and reviewed there and in Nature. This example was from the library of Brooklyn mathematics teacher, collector and historian of mathematics L. Leland Locke. There is no indication that the product proved popular.

References:

John Sawyer, “Improvement in the Means of Obtaining Arithmetical Results,” U.S. Patent 208037, September 17, 1878.

This is one of the earliest gratings made by Lewis M. Rutherfurd, and one of three that the pioneer astrophysicist, Henry Draper, acquired in the fall of 1872. The glass plate measures 1⅜ inches square and is marked "Nov. 19, 1872, 6480 per inch L. M. Rutherfurd."

The instrument consists of three concentric brass discs, a brass marker, a steel stop, and a wooden handle (instrument must be removed from box to find handle). Each brass disc has the numbers from 0 to 99 stamped around the edge. The two inner discs both have a circle of 100 holes just outside the numbers. The inner holes are used to add the last two digits of a number by rotation. Any hundreds value in the sum carries to the second set of holes, which are used to add hundreds and thousands places.

The machine is in a cylindrical wooden case with cover.

According to the Kirksville Missouri Democrat for July 26, 1888, by then Hart had sold 3500 of these devices and “he lately ordered one thousand more.”

References: U.S. Patent #199289

P. Kidwell, "Adders Made and Used in the United States," Rittenhouse, 1994, 8:78-96.

This 56-page paper pamphlet, copyrighted in 1881, has the full title A Revised Key to Gould's Patent Arithmetical Frame; Containing Much New and Valuable Matter, Including Common Fractions, Percentage, and the Metric System. It has a variety of problems in addition, subtraction, multiplication, division and decimal fractions that could be set up on a teaching device called Gould's patent arithmetical frame, along with answers. A section of the pamphlet discusses the metric system, and a variety of other arithmetic problems are included.

On the cover, Gould’s address is given as 72 Murray St., New York. This address is crossed out and Chatham, N.J., is written in in ink.

For a related object, see 1994.0038.01. For related correspondence, see 1994.0038.03.